Progressive refinement rendering of implicit surfaces

The visualisation of implicit surfaces can be an inefficient task when such surfaces are complex and highly detailed. Visualising a surface by first converting it to a polygon mesh may lead to an excessive polygon count. Visualising a surface by direct ray casting is often a slow procedure. In this paper we present a progressive refinement renderer for implicit surfaces that are Lipschitz continuous. The renderer first displays a low resolution estimate of what the final image is going to be and, as the computation progresses, increases the quality of this estimate at an interactive frame rate. This renderer provides a quick previewing facility that significantly reduces the design cycle of a new and complex implicit surface. The renderer is also capable of completing an image faster than a conventional implicit surface rendering algorithm based on ray casting

Progressive surface modeling scheme from unorganised curves

This paper presents a novel surface modelling scheme to construct a freeform surface progressively from unorganised curves representing the boundary and interior characteristic curves. The approach can construct a base surface model from four ordinary or composite boundary curves and support incremental surface updating from interior characteristic curves, some of which may not be on the final surface. The base surface is first constructed as a regular Coons surface and upon receiving an interior curve sketch, it is then updated. With this progressive modelling scheme, a final surface with multiple sub-surfaces can be obtained from a set of unorganised curves and transferred to commercial surface modelling software for detailed modification. The approach has been tested with examples based on 3D motion sketches; it is capable of dealing with unorganised design curves for surface modelling in conceptual design. Its limitations have been discussed

Nondestructive determination of subsurface grain morphology

Recent progress in experimental and numerical methods enables to scrutinize simulated polycrystal surface micromechanics at high spatial resolution. For the correct interpretation of similarities and deviations between experiment and simulation, the consideration of subsurface grain morphology is imperative because of its significant impact on the surface layer boundary condition. A novel method is presented that coarsely scans a relatively large area for subsurface crystallite orientation up to depths of ~0.2 mm by means of differential aperture X-ray microscopy. The resulting point set is categorized into grains according to proximity in physical and orientation space. Reconstruction of the subsurface grain structure starts with a Voronoi tessellation using the categorized set as seed points. Progressive smoothing of the resulting ragged grain boundary surfaces is achieved through mean curvature flow. As it turns out that the reconstruction quality of the bulk and on the surface are related, the latter can serve as guidance for optimum subsurface reconstruction

A progressive refinement approach for the visualisation of implicit surfaces

Visualising implicit surfaces with the ray casting method is a slow procedure. The design cycle of a new implicit surface is, therefore, fraught with long latency times as a user must wait for the surface to be rendered before being able to decide what changes should be introduced in the next iteration. In this paper, we present an attempt at reducing the design cycle of an implicit surface modeler by introducing a progressive refinement rendering approach to the visualisation of implicit surfaces. This progressive refinement renderer provides a quick previewing facility. It first displays a low quality estimate of what the final rendering is going to be and, as the computation progresses, increases the quality of this estimate at a steady rate. The progressive refinement algorithm is based on the adaptive subdivision of the viewing frustrum into smaller cells. An estimate for the variation of the implicit function inside each cell is obtained with an affine arithmetic range estimation technique. Overall, we show that our progressive refinement approach not only provides the user with visual feedback as the rendering advances but is also capable of completing the image faster than a conventional implicit surface rendering algorithm based on ray casting

Visualising Basins of Attraction for the Cross-Entropy and the Squared Error Neural Network Loss Functions

Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method to visualise basins of attraction together with the associated stationary points via gradient-based random sampling. The proposed technique is used to perform an empirical study of the loss surfaces generated by two different error metrics: quadratic loss and entropic loss. The empirical observations confirm the theoretical hypothesis regarding the nature of neural network attraction basins. Entropic loss is shown to exhibit stronger gradients and fewer stationary points than quadratic loss, indicating that entropic loss has a more searchable landscape. Quadratic loss is shown to be more resilient to overfitting than entropic loss. Both losses are shown to exhibit local minima, but the number of local minima is shown to decrease with an increase in dimensionality. Thus, the proposed visualisation technique successfully captures the local minima properties exhibited by the neural network loss surfaces, and can be used for the purpose of fitness landscape analysis of neural networks.Comment: Preprint submitted to the Neural Networks journa

Evaluation of maximum rockfall dimensions based on probabilistic assessment of the penetration of the sliding planes into the slope

There is intrinsic difficulty in the investigation of the largest volume of rockfalls that is expected in an area, which lies in the small number of large events, in registrable times. The maximum credible rockfall size has been associated with the properties of the rock mass discontinuities, as they delimit detachable rock blocks, and in particular with the penetration of those discontinuities that comprise rockfall sliding planes. In highly fractured rock masses, the evaluation of the penetration remains an issue. A probabilistic methodology is proposed, to measure the penetration of potential sliding planes into the interior of a rocky slope. The main hypothesis of the method is that the sliding plane persistence is interrupted along its two directions, at the intersection with two lateral discontinuity sets, as the latter displaces the former. Due to the displacement, the sliding planes are formed by quasi-planes that contain a maximum number of spacings of the intersecting joints, hence their size is restricted. The methodology requires as an input the spacing of the intersecting joint sets. Its application to a granodiorite slope confirms that for the study site, there is a maximum volume of rockfalls, excluding the possibility of large stepped failures and rupture of rock bridges. The maximum calculated persistence for the two existing sliding planes in the study site is, respectively, 28.0 m and 48.5 m. The maximum calculated sliding plane surfaces are, accordingly, 282.5 m2 and 289.3 m2. These results are compared against the observed scar dimensions at the study site, which have been retrieved alternatively, by processing a LiDAR point cloud. The results from the two alternative sources are similar, indicating that the methodology can be efficiently used to assess the sliding plane persistence and the expected maximum rockfall magnitude at the study site.Peer ReviewedPostprint (published version